Compound Growth
Compound Annual Growth Rate
The constant annual rate at which an investment grows from a starting value to an ending value, smoothing out volatility.
Formula
CAGR = (Ending Value ÷ Starting Value)^(1 ÷ Years) − 1
Variables
Ending Value- Final investment amount
Starting Value- Initial investment amount
Years- Number of years between start and end
Worked Example
Scenario: $10,000 growing to $20,000 over 10 years has a CAGR of approximately 7.18%.
Steps:
- Divide 20,000 by 10,000 = 2.0
- Calculate 1 ÷ 10 = 0.1
- Raise 2.0 to the power of 0.1 = 1.0718
- Subtract 1 and express as percentage = 7.18%
When to Use This Formula
- Measure investment performance over multiple years
- Compare investment returns with volatility smoothed
- Annualize multi-year returns into a single rate
Limitations & Assumptions
- Hides year-to-year volatility and timing of drawdowns
- Assumes no contributions or withdrawals between start and end
- Sensitive to start and end dates
Common Questions
Can CAGR be negative?
Yes, when the ending value is below the starting value (but both remain positive).
Why must starting value be positive?
It is the divisor and base of the calculation; zero or negative values break the formula.
Compound growth and regular investing
- SIP future value formulaFormula
- Annualized return formulaFormula
- Annualized returnDefinition
- Dollar-cost averagingDefinition
- Compound interest vs SIPComparison
Reference note: This is an educational mathematical reference. The formula's applicability depends on assumptions, market conditions, and use case. Always verify results independently and consult domain experts for decisions.